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QuestionKevin and Greg inherit \43000each.After1year,howmuchmoredoesGreghavethanKevinifheearns43000 each. After 1 year, how much more does Greg have than Kevin if he earns 5.3 \%vs. vs. 1.7 \%$?

Studdy Solution

STEP 1

Assumptions1. Both Kevin and Greg inherit \$43000 each. . Kevin invests his inheritance in a savings account with an annual return of1.7%.
3. Greg invests his inheritance in a CD paying5.3% annually.
4. We want to find out how much more money Greg has than Kevin after1 year.

STEP 2

First, we need to calculate how much money Kevin has after1 year. We can do this by multiplying his initial amount by the annual return rate and adding this to the initial amount.
Kevin′s money=Initial amount+(Initial amounttimesAnnual return rate)Kevin's\, money = Initial\, amount + (Initial\, amount \\times Annual\, return\, rate)

STEP 3

Now, plug in the given values for the initial amount and annual return rate to calculate Kevin's money.
Kevin′s money=$43000+($43000times1.7%)Kevin's\, money = \$43000 + (\$43000 \\times1.7\%)

STEP 4

Convert the percentage to a decimal value.
1.7%=0.0171.7\% =0.017Kevin′s money=$43000+($43000times0.017)Kevin's\, money = \$43000 + (\$43000 \\times0.017)

STEP 5

Calculate Kevin's money after1 year.
Kevin′s money=$43000+($43000times0.017)=$43730Kevin's\, money = \$43000 + (\$43000 \\times0.017) = \$43730

STEP 6

Now, we need to calculate how much money Greg has after1 year. We can do this by multiplying his initial amount by the annual return rate and adding this to the initial amount.
Greg′s money=Initial amount+(Initial amounttimesAnnual return rate)Greg's\, money = Initial\, amount + (Initial\, amount \\times Annual\, return\, rate)

STEP 7

Now, plug in the given values for the initial amount and annual return rate to calculate Greg's money.
Greg′s money=$43000+($43000times5.3%)Greg's\, money = \$43000 + (\$43000 \\times5.3\%)

STEP 8

Convert the percentage to a decimal value.
5.3%=0.0535.3\% =0.053Greg′s money=$43000+($43000times0.053)Greg's\, money = \$43000 + (\$43000 \\times0.053)

STEP 9

Calculate Greg's money after year.
Greg′s money=$43000+($43000times.053)=$45229Greg's\, money = \$43000 + (\$43000 \\times.053) = \$45229

STEP 10

Now that we have the money each brother has after year, we can subtract Kevin's money from Greg's money to find out how much more money Greg has than Kevin.
More money=Greg′s money−Kevin′s moneyMore\, money = Greg's\, money - Kevin's\, money

STEP 11

Plug in the values for Greg's money and Kevin's money to calculate the difference.
More money=$45229−$43730More\, money = \$45229 - \$43730

STEP 12

Calculate the difference.
More money=$45229−$43730=$1499More\, money = \$45229 - \$43730 = \$1499Greg has \$1499 more than Kevin after year.

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